Eureka is a city in and the county seat of Greenwood County, Kansas, United States. As of the 2020 census, the population of the city was …Eureka is a city in and the county seat of Greenwood County, Kansas, United States. As of the 2020 census, the population of the city was 2,332. The first settlement at Eureka was in 1857. The first post office in Eureka was established in August 1858. Eureka was laid out in 1867, and it was incorporated in 1870. The city is named from the Greek expression Eureka, meaning "I have found it".